Finite Group Databasebeta

← C2×#11735191 #13521880

Subgroups — C2×#11735191 #13521880

Order 1792.

2942 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D7×C4⋊C4C211yesmaximal, characteristic
2C22×#6452C211yesmaximal, characteristic, complemented
3C2×C7×#398C211yesmaximal, characteristic, complemented
4C2×#89761C211yesmaximal, characteristic
5C2×#89761C211yesmaximal, characteristic
6C2×#89759C211yesmaximal, characteristic
7C2×#89758C211yesmaximal, characteristic, complemented
8C2×#89744C211yesmaximal, characteristic, complemented
9C2×#89744C211yesmaximal, characteristic, complemented
10#11735191C2116yesmaximal, direct product factor
11C2×#89439C211yesmaximal, characteristic
12C2×#89439C211yesmaximal, characteristic
13C2×#89432C211yesmaximal, characteristic, complemented
14C2×#89429C211yesmaximal, characteristic, complemented
15C2×#89422C211yesmaximal, characteristic, complemented
16C2×#89438C211yesmaximal, characteristic
17C23×C4×D7C2211yescharacteristic
18C23×C4×D7C2211yescharacteristic
19C23×C4×D7C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C7×C4⋊C4C2211yescharacteristic
23C22×C7×C4⋊C4C2211yescharacteristic
24C22×(C2×D7)⋊C4C2211yescharacteristic
25C22×(C2×D7)⋊C4C2211yescharacteristic
26C22×(C2×D7)⋊C4C2211yescharacteristic
27C22×(C2×D7)⋊C4C2211yescharacteristic
28C22×C4⋊Dic7C2211yescharacteristic
29C22×C4⋊Dic7C2211yescharacteristic
30C22×Dic7⋊C4C2211yescharacteristic
31C22×Dic7⋊C4C2211yescharacteristic
32C22×Dic7⋊C4C2211yescharacteristic
33C22×Dic7⋊C4C2211yescharacteristic
34C22×Dic7⋊C4C2211yescharacteristic
35C22×Dic7⋊C4C2211yescharacteristic
36C22×Dic7⋊C4C2211yescharacteristic
37C22×Dic7⋊C4C2211yescharacteristic
38C22×C4×Dic7C2211yescharacteristic
39C22×C4×Dic7C2211yescharacteristic
40C2×D7×C4⋊C4—28no—
41C2×D7×C4⋊C4C2218yes—
42C2×#6452—28no—
43C2×#6452C2218yescomplemented
44C7×#398C2218yescomplemented
45C2×C7×#95C2211yescharacteristic
46C2×C7×#95C2211yescharacteristic
47C2×C7×#95C2211yescharacteristic
48C2×C7⋊#95C2211yescharacteristic
49C2×C7⋊#95C2211yescharacteristic
50C2×C7⋊#95C2211yescharacteristic
51C2×C7⋊#95C2211yescharacteristic
52C2×C7⋊#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54C2×C7⋊#95C2211yescharacteristic
55C2×C7⋊#95C2211yescharacteristic
56C2×C7⋊#95C2211yescharacteristic
57#89761C2218yes—
58#89761C2218yes—
59#89759C2218yes—
60#89758C2218yescomplemented
61#89744C2218yescomplemented
62#89744C2218yescomplemented
63#89439C2218yes—
64#89439C2218yes—
65#89438C2218yes—
66#89432C2218yescomplemented
67#89429C2218yescomplemented
68#89422C2218yescomplemented
69C2×#2442—71nomaximal, Sylow
70C24×D7C2311yescharacteristic
71C23×C4×C7C2311yescharacteristic
72C23×C4×C7C2311yescharacteristic
73C23×C4×C7C2311yescharacteristic
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C23×Dic7C2311yescharacteristic
79C23×Dic7C2311yescharacteristic
80C23×Dic7C2311yescharacteristic
81C23×Dic7C2311yescharacteristic
82C23×Dic7C2311yescharacteristic
83C23×Dic7C2311yescharacteristic
84C23×Dic7C2311yescharacteristic
85C22×C4×D7—24no—
86C22×C4×D7—24no—
87C22×C4×D7—24no—
88C22×C4×D7—24no—
89C22×C4×D7—24no—
90C22×C4×D7—24no—
91C22×C4×D7—42no—
92C22×C4×D7—42no—
93C22×C4×D7Q818yes—
94C22×C4×D7C2314yes—
95C22×C4×D7C2314yes—
96C22×C4×D7C2314yes—
97C2×C7×C4⋊C4—24no—
98C2×C7×C4⋊C4—24no—
99C2×C7×C4⋊C4—42no—
100C2×C7×C4⋊C4—42no—
101C2×C7×C4⋊C4C2314yes—
102C2×C7×C4⋊C4C2314yes—
103C2×C7×C4⋊C4C2314yes—
104C2×C7×C4⋊C4C2314yes—
105C2×(C2×D7)⋊C4—24no—
106C2×(C2×D7)⋊C4—24no—
107C2×(C2×D7)⋊C4—24no—
108C2×(C2×D7)⋊C4—24no—
109C2×(C2×D7)⋊C4C2314yes—
110C2×(C2×D7)⋊C4C2314yes—
111C2×(C2×D7)⋊C4C2314yes—
112C2×(C2×D7)⋊C4C2314yes—
113C2×C4⋊Dic7—24no—
114C2×C4⋊Dic7—24no—
115C2×C4⋊Dic7C2314yes—
116C2×C4⋊Dic7C2314yes—
117C2×Dic7⋊C4—24no—
118C2×Dic7⋊C4—24no—
119C2×Dic7⋊C4—24no—
120C2×Dic7⋊C4—24no—
121C2×Dic7⋊C4—24no—
122C2×Dic7⋊C4—42no—
123C2×Dic7⋊C4—42no—
124C2×Dic7⋊C4D418yes—
125C2×Dic7⋊C4C2314yes—
126C2×Dic7⋊C4C2314yes—
127C2×Dic7⋊C4C2314yes—
128C2×Dic7⋊C4C2314yes—
129C2×Dic7⋊C4C2314yes—
130C2×Dic7⋊C4C2314yes—
131C2×Dic7⋊C4C2314yes—
132C2×Dic7⋊C4C2314yes—
133C2×C4×Dic7—24no—
134C2×C4×Dic7—24no—
135C2×C4×Dic7C2314yes—
136C2×C4×Dic7C2314yes—
137D7×C4⋊C4—232no—
138#6452—232no—
139C7×#95C2314yes—
140C7×#95C2314yes—
141C7×#95C2314yes—
142C7⋊#95C2314yes—
143C7⋊#95C2314yes—
144C7⋊#95C2314yes—
145C7⋊#95C2314yes—
146C7⋊#95C2314yes—
147C7⋊#95C2314yes—
148C7⋊#95C2314yes—
149C7⋊#95C2314yes—
150C7⋊#95C2314yes—
151C22×#125—71no—
152C23×C4⋊C4—71no—
153#2442—716no—
154C2×#400—71no—
155C2×#400—71no—
156C2×#398—71no—
157C2×#398D711yescharacteristic, complemented
158C2×#389—71no—
159C2×#389—71no—
160C2×#385—71no—
161C2×#385—71no—
162C2×#382—71no—
163C2×#380—71no—
164C2×#380—71no—
165C2×#380—71no—
166C2×C4×C22⋊C4—71no—
167C24×C7C2411yescharacteristic
168C23×D7—22no—
169C23×D7—22no—
170C23×D7—22no—
171C23×D7—22no—
172C23×D7C2×Q814yes—
173C23×D7#4114yes—
174C23×D7#4114yes—
175C23×D7C2412yes—
176C22×C4×C7—22no—
177C22×C4×C7—22no—
178C22×C4×C7—22no—
179C22×C4×C7—22no—
180C22×C4×C7—22no—
181C22×C4×C7—22no—
182C22×C4×C7—22no—
183C22×C4×C7—22no—
184C22×C4×C7—22no—
185C22×C4×C7—22no—
186C22×C4×C7—22no—
187C22×C4×C7—22no—
188C22×C4×C7—22no—
189C22×C4×C7—22no—
190C22×C4×C7—22no—
191C22×C4×C7—22no—
192C22×C4×C7—22no—
193C22×C4×C7—22no—
194C22×C4×C7—22no—
195C22×C4×C7C2×D414yes—
196C22×C4×C7C2×Q814yes—
197C22×C4×C7C2412yes—
198C22×C4×C7C2412yes—
199C22×C4×C7C2412yes—
200C22×C4×C7C2412yes—
201C22×C4×C7C2412yes—
202C22×C4×C7C2412yes—
203C22×C4×C7C2412yes—
204C22×Dic7—22no—
205C22×Dic7—22no—
206C22×Dic7—22no—
207C22×Dic7—22no—
208C22×Dic7—22no—
209C22×Dic7—22no—
210C22×Dic7—22no—
211C22×Dic7—22no—
212C22×Dic7—22no—
213C22×Dic7—22no—
214C22×Dic7—22no—
215C22×Dic7—22no—
216C22×Dic7—22no—
217C22×Dic7—22no—
218C22×Dic7—22no—
219C22×Dic7—22no—
220C22×Dic7—22no—
221C22×Dic7C2×D414yes—
222C22×Dic7C2×D414yes—
223C22×Dic7C2×Q814yes—
224C22×Dic7#4114yes—
225C22×Dic7C2412yes—
226C22×Dic7C2412yes—
227C22×Dic7C2412yes—
228C22×Dic7C2412yes—
229C22×Dic7C2412yes—
230C22×Dic7C2412yes—
231C22×Dic7C2412yes—
232C2×C4×D7—232no—
233C2×C4×D7—28no—
234C2×C4×D7—28no—
235C2×C4×D7—28no—
236C2×C4×D7—28no—
237C2×C4×D7—28no—
238C2×C4×D7—28no—
239C2×C4×D7—44no—
240C2×C4×D7—44no—
241C2×C4×D7—416no—
242C2×C4×D7—416no—
243C2×C4×D7C2×Q8116yes—
244C7×C4⋊C4—28no—
245C7×C4⋊C4—28no—
246C7×C4⋊C4—44no—
247C7×C4⋊C4—44no—
248(C2×D7)⋊C4—28no—
249(C2×D7)⋊C4—28no—
250(C2×D7)⋊C4—28no—
251(C2×D7)⋊C4—28no—
252C4⋊Dic7—28no—
253C4⋊Dic7—28no—
254Dic7⋊C4—28no—
255Dic7⋊C4—28no—
256Dic7⋊C4—28no—
257Dic7⋊C4—28no—
258Dic7⋊C4—28no—
259Dic7⋊C4—44no—
260Dic7⋊C4—44no—
261Dic7⋊C4C2×D4116yes—
262C4×Dic7—28no—
263C4×Dic7—28no—
264C24×C4—71no—
265C24×C4—71no—
266C24×C4—71no—
267C2×#125—78no—
268C2×#125—148no—
269C22×C4⋊C4—71no—
270C22×C4⋊C4—71no—
271C22×C4⋊C4—71no—
272C22×C4⋊C4—71no—
273C22×C4⋊C4—71no—
274C22×C4⋊C4—71no—
275C22×C4⋊C4—71no—
276C22×C4⋊C4—71no—
277C22×C4⋊C4—71no—
278C22×C4⋊C4—71no—
279C22×C4⋊C4—78no—
280C22×C4⋊C4—148no—
281C22×C4⋊C4C2×D711yescharacteristic
282C22×C4⋊C4C2×D711yescharacteristic
283C22×C4⋊C4C2×D711yescharacteristic
284C22×C4⋊C4C2×D711yescharacteristic
285C22×C22⋊C4—71no—
286C22×C22⋊C4—71no—
287C22×C22⋊C4—71no—
288C22×C22⋊C4—71no—
289C22×C42—71no—
290C22×C42—71no—
291#400—78no—
292#400—78no—
293#398—78no—
294#398C2×D718yescomplemented
295#389—78no—
296#389—78no—
297#385—78no—
298#385—78no—
299#382—78no—
300#380—78no—
301#380—78no—
302#380—78no—
303C4×C22⋊C4—78no—
304C2×#95—71no—
305C2×#95—71no—
306C2×#95—71no—
307C2×#95—71no—
308C2×#95—71no—
309C2×#95—71no—
310C2×#95—71no—
311C2×#95—71no—
312C2×#95—71no—
313C2×#95C2×D711yescharacteristic
314C2×#95C2×D711yescharacteristic
315C2×#95C2×D711yescharacteristic
316C23×C7C22×D412yes—
317C23×C7C22×Q812yes—
318C23×C7C2×#4112yes—
319C23×C7C2×#4112yes—
320C23×C7C2×#4112yes—
321C23×C7H(5,𝔽2)12yes—
322C23×C72−1+412yes—
323C23×C7C2511yescharacteristic
324C22×D7—28no—
325C22×D7—28no—
326C22×D7—28no—
327C22×D7—28no—
328C22×D7—28no—
329C22×D7—28no—
330C22×D7—22no—
331C22×D7—22no—
332C22×D7—22no—
333C22×D7—22no—
334C22×D7#125116yescomplemented
335C22×D7C22×Q814yes—
336C22×D7C2×#4114yes—
337C22×D7C2×#4114yes—
338C2×C4×C7—28no—
339C2×C4×C7—28no—
340C2×C4×C7—22no—
341C2×C4×C7—22no—
342C2×C4×C7—22no—
343C2×C4×C7—22no—
344C2×C4×C7—22no—
345C2×C4×C7—22no—
346C2×C4×C7—22no—
347C2×C4×C7—22no—
348C2×C4×C7—22no—
349C2×C4×C7—22no—
350C2×C4×C7—22no—
351C2×C4×C7—22no—
352C2×C4×C7—22no—
353C2×C4×C7—22no—
354C2×C4×C7—22no—
355C2×C4×C7—22no—
356C2×C4×C7—22no—
357C2×C4×C7—22no—
358C2×C4×C7—22no—
359C2×C4×C7—44no—
360C2×C4×C7—44no—
361C2×C4×C7—44no—
362C2×C4×C7—44no—
363C2×C4×C7—44no—
364C2×C4×C7C22×D414yes—
365C2×C4×C7C22×Q814yes—
366C2×Dic7—28no—
367C2×Dic7—22no—
368C2×Dic7—22no—
369C2×Dic7—22no—
370C2×Dic7—22no—
371C2×Dic7—22no—
372C2×Dic7—22no—
373C2×Dic7—22no—
374C2×Dic7—22no—
375C2×Dic7—22no—
376C2×Dic7—22no—
377C2×Dic7—22no—
378C2×Dic7—22no—
379C2×Dic7—22no—
380C2×Dic7—22no—
381C2×Dic7—22no—
382C2×Dic7—22no—
383C2×Dic7—22no—
384C2×Dic7—44no—
385C2×Dic7—44no—
386C2×Dic7—44no—
387C2×Dic7—44no—
388C2×Dic7—44no—
389C2×Dic7C22⋊Q8116yes—
390C2×Dic7C22×D414yes—
391C2×Dic7C22×D414yes—
392C2×Dic7C22×Q814yes—
393C2×Dic7C2×#4114yes—
394C4×D7—232no—
395C4×D7—416no—
396C4×D7—416no—
397C25—71no—
398C23×C4—71no—
399C23×C4—71no—
400C23×C4—78no—
401C23×C4—74no—
402C23×C4—71no—
403C23×C4—71no—
404C23×C4—71no—
405C23×C4—71no—
406C23×C4—71no—
407C23×C4—74no—
408C23×C4—74no—
409C23×C4—144no—
410C23×C4—144no—
411C23×C4—144no—
412C23×C4—144no—
413C23×C4—144no—
414C23×C4—144no—
415C23×C4—282no—
416C23×C4—282no—
417C23×C4C22×D711yescharacteristic
418C23×C4C22×D711yescharacteristic
419C23×C4C22×D711yescharacteristic
420C23×C4C22×D711yescharacteristic
421C23×C4C22×D711yescharacteristic
422C23×C4C22×D711yescharacteristic
423C23×C4C22×D711yescharacteristic
424#125—1432no—
425C2×C4⋊C4—24no—
426C2×C4⋊C4—24no—
427C2×C4⋊C4—42no—
428C2×C4⋊C4—42no—
429C2×C4⋊C4—78no—
430C2×C4⋊C4—74no—
431C2×C4⋊C4—74no—
432C2×C4⋊C4—74no—
433C2×C4⋊C4—74no—
434C2×C4⋊C4—74no—
435C2×C4⋊C4—74no—
436C2×C4⋊C4—74no—
437C2×C4⋊C4—74no—
438C2×C4⋊C4—74no—
439C2×C4⋊C4—74no—
440C2×C4⋊C4—1432no—
441C2×C4⋊C4—144no—
442C2×C4⋊C4—144no—
443C2×C4⋊C4—144no—
444C2×C4⋊C4—144no—
445C2×C4⋊C4—144no—
446C2×C4⋊C4—144no—
447C2×C4⋊C4—144no—
448C2×C4⋊C4—282no—
449C2×C4⋊C4—282no—
450C2×C4⋊C4C22×D714yes—
451C2×C4⋊C4C22×D714yes—
452C2×C4⋊C4C22×D714yes—
453C2×C4⋊C4C22×D714yes—
454C2×C22⋊C4—74no—
455C2×C22⋊C4—74no—
456C2×C22⋊C4—74no—
457C2×C22⋊C4—74no—
458C2×C22⋊C4—144no—
459C2×C22⋊C4—144no—
460C2×C22⋊C4—144no—
461C2×C22⋊C4—144no—
462C2×C42—74no—
463C2×C42—74no—
464C2×C42—144no—
465C2×C42—144no—
466#95—74no—
467#95—74no—
468#95—74no—
469#95—74no—
470#95—74no—
471#95—74no—
472#95—74no—
473#95—74no—
474#95—74no—
475#95C22×D714yes—
476#95C22×D714yes—
477#95C22×D714yes—
478C22×C7C2×C22⋊Q814yes—
479C22×C7C2×#12514yes—
480C22×C7#54414yes—
481C22×C7#54614yes—
482C22×C7#54814yes—
483C22×C7#55214yes—
484C22×C7#55314yes—
485C22×C7C23×D411yescharacteristic
486C22×C7C23×Q811yescharacteristic
487C22×C7C22×#4111yescharacteristic
488C22×C7C22×#4111yescharacteristic
489C22×C7C22×#4111yescharacteristic
490C22×C7C2×H(5,𝔽2)11yescharacteristic
491C22×C7C2×2−1+411yescharacteristic
492C2×D7—24no—
493C2×D7—24no—
494C2×D7—24no—
495C2×D7—24no—
496C2×D7—232no—
497C2×D7—24no—
498C2×D7—24no—
499C2×D7C2×#12518yescomplemented
500C4×C7—24no—
501C4×C7—24no—
502C4×C7—42no—
503C4×C7—42no—
504C4×C7—42no—
505C4×C7—42no—
506C4×C7—42no—
507Dic7—24no—
508Dic7—42no—
509Dic7—42no—
510Dic7—42no—
511Dic7—42no—
512Dic7—42no—
513Dic7C2×C22⋊Q818yes—
514C24—74no—
515C24—74no—
516C24—74no—
517C24—72no—
518C24—142no—
519C24—142no—
520C24—142no—
521C24—142no—
522C24C23×D711yescharacteristic
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—74no—
543C22×C4—74no—
544C22×C4—74no—
545C22×C4—72no—
546C22×C4—74no—
547C22×C4—72no—
548C22×C4—716no—
549C22×C4—72no—
550C22×C4—72no—
551C22×C4—72no—
552C22×C4—72no—
553C22×C4—72no—
554C22×C4—148no—
555C22×C4—1432no—
556C22×C4—148no—
557C22×C4—148no—
558C22×C4—148no—
559C22×C4—148no—
560C22×C4—142no—
561C22×C4—142no—
562C22×C4—142no—
563C22×C4—142no—
564C22×C4—142no—
565C22×C4—142no—
566C22×C4—142no—
567C22×C4—142no—
568C22×C4—142no—
569C22×C4—142no—
570C22×C4—142no—
571C22×C4—142no—
572C22×C4—142no—
573C22×C4—142no—
574C22×C4—142no—
575C22×C4—142no—
576C22×C4—142no—
577C22×C4—148no—
578C22×C4—284no—
579C22×C4—284no—
580C22×C4—2816no—
581C22×C4—2816no—
582C22×C4D4×D714yes—
583C22×C4Q8×D714yes—
584C22×C4C23×D712yes—
585C22×C4C23×D712yes—
586C22×C4C23×D712yes—
587C22×C4C23×D712yes—
588C22×C4C23×D712yes—
589C22×C4C23×D712yes—
590C22×C4C23×D712yes—
591C4⋊C4—28no—
592C4⋊C4—28no—
593C4⋊C4—44no—
594C4⋊C4—44no—
595C4⋊C4—716no—
596C4⋊C4—148no—
597C4⋊C4—148no—
598C4⋊C4—148no—
599C4⋊C4—148no—
600C4⋊C4—148no—
601C4⋊C4—148no—
602C4⋊C4—148no—
603C4⋊C4—284no—
604C4⋊C4—284no—
605C22⋊C4—148no—
606C22⋊C4—148no—
607C22⋊C4—148no—
608C22⋊C4—148no—
609C42—148no—
610C42—148no—
611C2×C7#244218yescomplemented
612C2×C7C22×C22⋊Q811yescharacteristic
613C2×C7C22×#12511yescharacteristic
614C2×C7C2×#54411yescharacteristic
615C2×C7C2×#54611yescharacteristic
616C2×C7C2×#54811yescharacteristic
617C2×C7C2×#55211yescharacteristic
618C2×C7C2×#55311yescharacteristic
619D7—28no—
620C23—716no—
621C23—74no—
622C23—74no—
623C23—74no—
624C23—148no—
625C23—148no—
626C23—148no—
627C23—148no—
628C23—148no—
629C23—142no—
630C23—148no—
631C23—142no—
632C23—142no—
633C23—142no—
634C23C2×D4×D712yes—
635C23#654812yes—
636C23C2×Q8×D712yes—
637C23#655112yes—
638C23D7×#4112yes—
639C23D7×#4112yes—
640C23D7×#4112yes—
641C23C24×D711yescharacteristic
642C2×C4—28no—
643C2×C4—28no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—44no—
664C2×C4—44no—
665C2×C4—44no—
666C2×C4—44no—
667C2×C4—44no—
668C2×C4—716no—
669C2×C4—74no—
670C2×C4—74no—
671C2×C4—74no—
672C2×C4—74no—
673C2×C4—1432no—
674C2×C4—148no—
675C2×C4—142no—
676C2×C4—142no—
677C2×C4—142no—
678C2×C4—142no—
679C2×C4—142no—
680C2×C4—142no—
681C2×C4—142no—
682C2×C4—142no—
683C2×C4—142no—
684C2×C4—142no—
685C2×C4—142no—
686C2×C4—142no—
687C2×C4—142no—
688C2×C4—142no—
689C2×C4—142no—
690C2×C4—142no—
691C2×C4—142no—
692C2×C4—2816no—
693C2×C4—2816no—
694C2×C4—284no—
695C2×C4—284no—
696C2×C4—284no—
697C2×C4—284no—
698C2×C4—284no—
699C2×C4C2×D4×D714yes—
700C2×C4C2×Q8×D714yes—
701C7C2×#244211yescharacteristic, complemented, Sylow
702C22—78no—
703C22—144no—
704C22—144no—
705C22—144no—
706C22—144no—
707C22—144no—
708C22—1432no—
709C22—144no—
710C22#9030114yes—
711C22D7×C22⋊Q814yes—
712C22#9032414yes—
713C22#9035214yes—
714C22D7×#12514yes—
715C22#9038414yes—
716C22#9042014yes—
717C22C22×D4×D711yescharacteristic
718C22C2×#654811yescharacteristic
719C22C22×Q8×D711yescharacteristic
720C22C2×#655111yescharacteristic
721C22C2×D7×#4111yescharacteristic
722C22C2×D7×#4111yescharacteristic
723C22C2×D7×#4111yescharacteristic
724C4—24no—
725C4—24no—
726C4—42no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—78no—
732C4—144no—
733C4—282no—
734C4—282no—
735C4—282no—
736C4—282no—
737C4—282no—
738C2—148no—
739C2#1173519118yesdirect product factor
740C2C2×#9030111yescharacteristic
741C2C2×D7×C22⋊Q811yescharacteristic
742C2C2×#9032411yescharacteristic
743C2C2×#9035211yescharacteristic
744C2C2×D7×#12511yescharacteristic
745C2C2×#9038411yescharacteristic
746C2C2×#9042011yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#398C2
socleC24×C7C24
prime radicalC24×D7C23
hypercenterC2×#398D7
hypocenterC7C2×#2442
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#398

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C22×#6452C2semidirect
3. C2×C7×#398C2semidirect
7. C2×#89758C2semidirect
8. C2×#89744C2semidirect
9. C2×#89744C2semidirect
10. #11735191C2direct (N × H)
13. C2×#89432C2semidirect
14. C2×#89429C2semidirect
15. C2×#89422C2semidirect
43. C2×#6452C22semidirect
44. C7×#398C22semidirect
60. #89758C22semidirect
61. #89744C22semidirect
62. #89744C22semidirect
66. #89432C22semidirect
67. #89429C22semidirect
68. #89422C22semidirect
157. C2×#398D7semidirect
294. #398C2×D7semidirect
334. C22×D7#125semidirect
499. C2×D7C2×#125semidirect
611. C2×C7#2442semidirect
701. C7C2×#2442semidirect
739. C2#11735191direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×D7×C4⋊C42
C22×#64522
C2×C7×#3982
C2×#897612
C2×#897592
C2×#897582
C2×#897442
#117351912
C2×#894392
C2×#894322
C2×#894292
C2×#894222
C2×#894382
C2×#24427